FOM: Re: V=L vs. PD

[John Steel]

This is a reply to Harvey's last post on the subject. 

I still don't know whether I'm arguing with Harvey, or with the "normal
mathematician". My impression from Harvey's post is
that the normal mathematician, whoever he is, is a small-minded
character interested in nothing but his own work, who hasn't thought much
at all about what we want out of our axioms. In particular, he doesn't
realize that the axioms are there to make mathematical work possible, not
to force work of some kind or other to be done. Perhaps we should spend
some time trying to enlighten this character, but why should he be the
focus of this discussion? 

Obviously theories need applications. I have a high opinion of the work
Harvey has done in applying large cardinal theory. But it is absurd to
suggest that until this work had been done, it would have been rational to
reject large cardinal theory, to prohibit or discourage its development.
Harvey's own work would never have been done in that case. Mahlo cardinals
would never have been discovered by looking through the lens of Boolean
Relation Theory. Large cardinal hypotheses flow from general foundational
considerations, and by developing the extensive theory around them in a
natural way, we only make important applications more likely. 

John Steel